Joint distribution of Busemann functions for the corner growth model

Stochastics Seminar
Thursday, February 28, 2019 - 3:05pm
1 hour (actually 50 minutes)
Skiles 006
Indiana University, Bloomington

We present the joint distribution of the Busemann functions, in all directions of growth, of the exactly solvable corner growth model (CGM). This gives a natural coupling of all stationary CGMs and leads to new results about geodesics. Properties of this joint distribution are accessed by identifying it as the unique invariant distribution of a multiclass last passage percolation model. This is joint work with Timo Seppäläinen.